Go straight for First Blood. I am not a fan of poking enemy champion for a long period of time in the beginning.

Don`t be Scared of being Ganked, you`re stronger. Fight back! you will die and yor Passive (Blood Well) will bring you back to life, so you can finish them if you dealt good damage before you died.

My strategy is to draw the first blood as soon as possible, so my build starts with 9+9+9 Attack Speed & 1+1+1 Life Steal.
Some may say it seems problematic in Lane to bee Full AS LS without Armor, it works great.

I think everything about my Mastery Point usage is clear.

Aatrox is Off-Tank !!! Start with Doran`s Blade STACK so you have a decent HP in Lane and your Life Steal works more than enough in Early Game.

Start with your E because thats how you gona poke opposit teams Champ. Works extra Perfect if your Enemy is a Meele (Non-Ranged) Champ. But try not to Skill Farm. You may have no mana, but it takes your HP instead. Don`t just go for the final hit on minions. try to attack as much as possible. Blood Thirst (W) will heal you every 3rd hit and not to forget the fact that you Stacked your Life Steal. When Above 50% HP use your W (Passive Skill) as Blood Price.
Every 3rd hit will take some of your HP but deal some extra damage on target. When under 50% HP switch to Blood Thirst which will heal you every 3rd hit. Once FED, leave your W in Blood Price. Your Life Steal will be more than the HP damage you get from your W. Last skill to upgrade is your Q. It`s the reason of Aatrox`s Nick Name "The DUNKMASTER"
Your ulti gives you extra Range, AS & AD so don`t save it up too much. Use it everytime you hit an Enemy.

After taking the 1st tower, Push to 2nd tower and go Mid.

HERE THE GAME BEGINS
Hope I could help you.

PREPARE YOUSELF FOR BATTLE..